EPJ Web of Conferences
Volume 3, 201019th International IUPAP Conference on Few-Body Problems in Physics
|Number of page(s)||5|
|Published online||12 April 2010|
Deﬁnition of an appropriate free dynamics and the physical S-matrix in multichannel hyperradial adiabatic scattering
Bogoliubov Laboratory of Theoretical Physics , Joint Institute
for Nuclear Research, 141980
Dubna, Moscow, Russia
2 Kitasato University, 1-15-1 Kitasato, Sagamihara, Kanagawa 228-8555, Japan
3 Institut für Physik, Universität Mainz, D-55099, Mainz, Germany
a e-mail: firstname.lastname@example.org
In the hyperradial adiabatic (HA) treatment of the three-body problem the total wave function is i expanded as ΨHA(R, ξ, η) = R−5/2 ∑iχi(R)φi(R|ξ, η),where R denotes the hyperradius and (ξ , η) are internal hyperangles. Integration over ξ and η converts the Schrödinger equation into a system of coupled hyperradial equations. It is a well-known fact that, within the HA approach, the non-adiabatic corrections that couple channels converging to the same asymptotic conﬁguration can show an unphysical long-range behavior ∼ 1/R. Though the latter is of purely kinematic origin and arises from the use of the hyperradius instead of the pertinent Jacobi variables, it is nevertheless the source of the considerable diﬃculties inherent in this approach. Here we propose, following the analysis of [1, 2], to deﬁne appropriate hyperradial-distorted free incoming and outgoing waves (H DF W ) that incorporate these unphysical long-range eﬀects. Using them the physical S−matrix can be found in a straightforward manner.
© Owned by the authors, published by EDP Sciences, 2010
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